Helping Children Learn Mathematics

Description

Title Page Copyright Page Contents About the authors Preface CHAPTER 1 School mathematics in achanging world Introduction 1.1 What is mathematics? 1.2 What determines the mathematics being taught? 1.3 Where can you turn? CHAPTER 2 Helping children learn mathematics with understanding Introduction 2.1 How can we support the diverse learners in our classrooms? 2.2 Meaningful connections between procedural and conceptual knowledge 2.3 How do children learn mathematics? 2.4 How can we help children make senseof mathematics? CHAPTER 3 Planning and teaching Introduction 3.1 Effective planning and preparation for teaching: using strategic questions to inform teaching practice 3.2 Planning for effective teaching 3.3 Levels of planning 3.4 Planning different types of lessons 3.5 Meeting the needs of all students 3.6 Assessment and analysis in planning CHAPTER 4 Enhancing learning and teaching through assessment and feedback Introduction 4.1 Enhancing learning and teaching 4.2 Gathering information on student learning 4.3 Ways to assess students’ learning and dispositions 4.4 Keeping records and communicating about assessments CHAPTER 5 Processes of doing mathematics Introduction 5.1 Problem solving 5.2 Reasoning and proof 5.3 Communication 5.4 Connections 5.5 Representations CHAPTER 6 Helping children with problem solving Introduction 6.1 What is a problem and what is problem solving? 6.2 Teaching mathematics through problem solving 6.3 Strategies for problem solving 6.4 The importance of looking back 6.5 Helping all students with problem solving CHAPTER 7 Counting and number sense in early childhood and primary years Introduction 7.1 Developing number sense 7.2 Counting principles 7.3 Counting strategies 7.4 Cardinal, ordinal and nominal numbers 7.5 Writing numerals CHAPTER 8 Extending number sense: place value Introduction 8.1 Our numeration system 8.2 Nature of place value 8.3 Beginning place value 8.4 Consolidating place value 8.5 Extending place value 8.6 Reading and writing numbers 8.7 Rounding CHAPTER 9 Operations: meanings and basic facts Introduction 9.1 Helping children develop number sense and computational fluency 9.2 Developing meanings for the operations 9.3 Mathematical properties 9.4 Overview of learning the basic facts 9.5 Thinking strategies for basic facts CHAPTER 10 Mental computation, calculators and estimation Introduction 10.1 Calculators 10.2 Mental computation 10.3 Estimation CHAPTER 11 Solving problems with written strategies Introduction 11.1 Learning strategies that lead to understanding 11.2 Addition 11.3 Subtraction 11.4 Multiplication 11.5 Division 11.6 Finding the balance between practice and proficiency CHAPTER 12 Fractions and decimals: meanings and operations Introduction 12.1 Conceptual development of fractions 12.2 Operations with fractions 12.3 Conceptual development of decimals 12.4 Operations with decimals CHAPTER 13 Ratio, proportion and percentages: meanings and applications Introduction 13.1 Ratios 13.2 Proportions 13.3 Percentages CHAPTER 14 Extending students with number theory Introduction 14.1 Number theory in primary school mathematics 14.2 Number theory topics for primary school students 14.3 Other number theory topics CHAPTER 15 Algebraic thinking Introduction 15.1 Problems, patterns and relations 15.2 Language and symbols of algebra 15.3 Modelling, generalising and justifying CHAPTER 16 Geometry Introduction 16.1 The geometry of 2-dimensional shapes and 3-dimensional objects 16.2 Locations and spatial relationships 16.3 Transformations 16.4 Visualisation and spatial reasoning CHAPTER 17 Measurement Introduction 17.1 The measurement process 17.2 Identifying attributes and comparing 17.3 Measurement concepts for all units 17.4 Measuring with informal units 17.5 Measuring with formal units 17.6 Applications including formulae 17.7 Comparing and converting measurements 17.8 Estimating measurements 17.9 Connecting attributes CHAPTER 18 Data analysis, statistics and probability Introduction 18.1 Formulating questions and collecting data 18.2 Organising and representing data 18.3 Analysing data: descriptive statistics 18.4 Interpreting results 18.5 Probability Appendix A Appendix B Appendix C EULA